When winding a coil of-wire on a rotating stub mandrel, irregularities in the winding mechanism and in the wire give rise to vibrations and in excursions of the wound coil from its axis of rotation. Vibration can also arise from other sources, such as a mechanism for periodically cutting the coil into predetermined lengths. It is known to damp such vibrations by applying pads or rollers to the rotating coil, but such damping means can damage the wire and is a source of friction. The severity of these vibrations increases with increasing rotational speed of the mandrel and of the coil and effectively limits the rotational speed of the mandrel to some 2,000 to 4,000 r.p.m. These vibrations can give rise to unevenly wound coils and deformed portions of coil where it is cut into desired lengths. Any method of effectively dampening such vibrations would contribute to higher productivity and lower manufacturing costs.